x(x+30)=90

Solution for x(x+30)=90 equation:

x(x+30)=90

We move all terms to the left:

x(x+30)-(90)=0

We multiply parentheses

x^2+30x-90=0

a = 1; b = 30; c = -90;
Δ = b2-4ac
Δ = 302-4·1·(-90)
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{35}}{2*1}=\frac{-30-6\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{35}}{2*1}=\frac{-30+6\sqrt{35}}{2}
$